I can click this link and it opens the file in Notepad++ like I intended. However, it doesn’t go to line 3686. Is there any way I can make this link or another format link open the file in Notepad++ and go to that line?

I don’t think it is possible using native npp functions.
What I can think of is using a scripting language like python script or lua script
and using the hotspotclick notification send by scintilla.
We would receive the location/position of this click event and could get the text
from that line. If your format is always the same I assume we could prepare such a script.
Let us know if you wanna go this way.

because the latest python script version tends to fail if installed by plugin manager
just double check if it has correctly installed on your side. Plugins->PythonScript->Show Console should report something like

Done - every time you start npp this script gets executed automatically.

What does the script?
It registers a callback for hotspotclick and bufferactivated notification. Once you click
on a link the callback gets executed and tries to get the text from the link.
If it starts with file:/// and has # in the line it is supposed to be a file link and gets
the details, file_to_load and line_in_file. Then it asks notepad to open that file.
If this is successful, npp sends a notification (bufferactivated) once the buffer has been loaded. Now the second part starts - it gets checked if this is the file we want
and if so we goto the line in question.
Currently I have no windows environment to test but under Linux(wine)
I do have a strange behavior. When the goto line is called some text before that
line gets selected. I hope this isn’t an issue under windows.

ok, one last change before going to bed.
Maybe there is text before and after the link, in such a case
it would break the logic. Here a solution which gets the link text only.
Replace callbackHOTSPOT… with this one